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We present new results on an optical implementation of Grover's quantumsearch algorithm. This extends previous work in which the transverse spatialmode of a light beam oscillates between a broad initial input shape and ahighly localized spike, which reveals the position of the tagged item. Thespike reaches its maximum intensity after $\sim\sqrt N$ round trips in a cavityequipped with two phase plates, where $N$ is the ratio of the surface area ofthe original beam and the area of the phase spot or tagged item. In ourredesigned experiment the search space is now two-dimensional. In the timedomain we demonstrate for the first time a multiple item search where the itemsappear directly as bright spots on the images of a gated camera. In acomplementary experiment we investigate the searching cavity in the frequencydomain. The oscillatory nature of the search algorithm can be seen as asplitting of cavity eigenmodes, each of which concentrates up to 50% of itspower in the bright spot corresponding to the solution.Comment: 16 pages in preprint format, 6 figures v2: some minor revision

Time- and frequency-domain solutions in an optical analogue of Grover's search algorithm